Trapezoidal rule quadrature is better than you would expect (2nd order) for periodic (even better for analytic and indeed entire, in this case) integrands. See

Trapezoidal rule quadrature is better than you would expect (2nd order) for periodic (even better for analytic and indeed entire, in this case) integrands. See this paper: http://eprints.maths.ox.ac.uk/1734/ http://eprints.maths.ox.ac.uk/1734/